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Please answer this question FULLY. There are THREE correct answers. Please answer in the form of A, B, C

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Assume that a simple random sample has been selected from a normally distributed population and test the given claim. State the final conclusion that addresses the original claim and select three correct choices. A machine dispenses a liquid drug into bottles in such a way that the standard deviation of the contents is 81 milliliters. A new machine is tested on a sample of 24 containers and the standard deviation for this sample group is found to be 26 milliliters. At the 0.05 level of significance, test the claim that the amounts dispensed by the new machine have a smaller standard deviation. SELECT ALL APPLICABLE CHOICES A) There is enough evidence to support the Claim By Hi: ơ<81 (claim) Ho: σ>81 C)There is enough evidence to reject the Ho D) There is NOT enough evidence to support the Claim E) H1 : σ< 26 (claim) Ho: σ>26 F) There is NOT enough evidence to reject the Ho G) None of these

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Step1: The summary stati stics are given below 24, α-0.05, and s 26 To, test whether the population standard deviation (σ) is less than 1 using the chi-square test to test the populati on standard deviati on State the null and alternative hypotheses: Ho : ơ281 (The population variance is equal to 81) Hı : σ-81 (The population variance is less than 81 Step 2: Select the distributi on to use We use the chi-square distribution to test a hypothesis about Step 3: Determine the rejection and nonrejection regions The significance level is 5%. The sign in Hı indicates that the test is left-tailed. The rejecti on regi on lies in left tail of the chi-square di stribution curve with the level of significance is α The degrees of freedom are 24-1 The critical value of x for 23 degrees of freedom for 23 df and 0.95 area in the right tail 13.09051 Step 4: Calculate the value of the test statistic The value of the test stati sticfor the sample variance is calculated as follows (n-1)s (24-1)676 6561 23(676) 6561 15548 6561 2.369761 x2.3697 Step 5: Make a decisi on Since, the P-value 10.000| < α-0.05. We do not reject the null hypothesis H0. The Classical Approach Since, the test stati stic is 2.3697 < We do not reject the null hypothesis H0 There is not sufficient evidence to reject the null hypothesis Ho. Step6: Select the opti on (D): There is not enough evi dence to support the claim Select the option (E): State the null and alternative hypotheses: Ho : σ281 (The population variance is equal to 81) H1 : σ 81 (The population variance is less than 81 Select the option (F): There is not enough evidenec to reject the Ho 0s3 13.09051

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